Trying to physically verify equation for Spring Mass model

[Ted Andresen]

I wanted to experimentally verify the step frequency’s (SF) dependence on Body Mass (BM). It appears in an equation I use to estimate leg-stiffness (kleg) for scenarios that I run through the model.

The expression is for the frequency of a mass bouncing vertically on a spring. This is similar to a subject running in-place with close to zero aerial phase.

The equation,

SF=(1/(2*PI))*SQRT(kleg/BM)

implies that if the BM increases, the SF should decrease according to 1/SQRT(BM).

If a subject while running very slowly, adds 20% to their BM using a weight jacket, then their step frequency should decrease by SQRT(1/1.2) or 8.7%. .

I have tried this myself, but I don’t have access to a weight jacket. I could only hand-hold an additional 10% of my BM while I ran slowly. Then, my SF dropped by 3%; I expected it to decrease by 5%.

I have looked for research on this issue, but I could not find any. Has anyone ever worked in this area? Or, are there any published articles on this topic?

Ted

[Chris Kirtley]

Re: Trying to physically verify equation for Spring Mass model

I would guess it's because the weights are not near the centre of mass, Ted. You are, in effect, using halteres:

https://www.youtube.com/watch?v=-K-0PU9K-Js

[Allan Carman]

Re: Trying to physically verify equation for Spring Mass model

Ted,

Could your leg stiffness have increased by 3.5% to go with the increase in mass of 10% to give a resultant 3% increase in SF?

Cheers
Allan

[Ted Andresen]

Re: Trying to physically verify equation for Spring Mass model

Chris: Thank you for the video link. Marcus Essa is truly an impressive athlete. When I did my initial experiments I held the hand weights tightly against my ilium, so there would only be a small but --- I am sure present -- halters effect.

Allan: I am not sure that bio-mechanical leg-stiffness could be related to the BM. All the physical systems I have dealt with followed Hooke’s Law. That and Newton’s equations are at the foundation of the spring mass model.

SFvsBM.png

I redid this experiment several times. With a weight belt tightly secured around my ilium, I able to get SF measurements (blue diamonds) that agreed with the theoretical values (red squares). I was surprised that the results were so close – experiments have NEVER worked-out that way in the past!

If anyone attempts do this experiment, they may want to use an 8-pocket weight-belt with 2 lb. (4.4 Kg) weights. They should also add extra supports or blocks under their tread-board to keep it from flexing during the stance phase. I performed my experiment at 3 mph (1.33 m/s, 20 min/mile, 12.4 min/km) just above the walk-run transition speed.

Thank you for your comments.

Ted

[Gerrard Farrell]

Re: Trying to physically verify equation for Spring Mass model

Hi Ted
I wondered if you had looked at this thread on the site and if so what you thought of the ideas -



Ground reaction forces and gait

I wonder if shortening the effective arm length during gait would increase step frequency -just a hunch . With regard to your first post ,would holding weights reduce arm swing amplitude compared to a non weight holding set up .

I don't have the expertise or equipment to look the idea of pelvic acceleration feeding energy into the bodies pendulums (arms legs ) to produce body segment co-ordination but if you did it could be interesting .

Regards

Gerry

[Ted Andresen]

Re: Trying to physically verify equation for Spring Mass model

Hi Gerry,

Yes I had followed at that very interesting discussion. Physics and modeling mechanical systems is my area, so part of discussion was beyond me.

The SM model functions in the sagittal plane, so it does not include rotational considerations about the vertical axis. I could not guess on the coupling between arm length and step frequency. I believe that the hip-hugging weight belt avoided that issue.

Thanks for your question.

Ted

[Young-Hui Chang]

Re: Trying to physically verify equation for Spring Mass model

Hi Ted, We did not address this issue directly, but we do present some data in the paper below that may be of help to you. We had a variety of conditions where we varied body weight and body mass independently during treadmill running (the bodyweight increase condition would match closest to what you are doing, I believe). Best of luck on an interesting problem!

Chang YH, Huang HW, Hamerski CM, Kram R. (2000) The independent effects of gravity and inertia on running mechanics. J Exp Biol 203: 229-238.
http://jeb.biologists.org/content/203/2/229

cheers,

Young-Hui

[Ted Andresen]

Re: Trying to physically verify equation for Spring Mass model

Hi Young-Hui,

Thank you for the link to your publication. It was an interesting read.

I was fascinated by the way you employed the climbing harness with the lead strips along with the elastic chord and winches to control the trolley. I think I can I can use that idea.

Ted

[Chris Kirtley]

Re: Trying to physically verify equation for Spring Mass model

Interestingly, I see the effects on walking are different:

https://www.researchgate.net/profile/John_De_Witt2/publication/5508825_The_effect_of_increasing_inertia_upon_vertical_ground_reaction_forces_and_temporal_kinematics_during_locomotion/links/5859ba5008ae64cb3d4944e0/The-effect-of-increasing-inertia-upon-vertical-ground-reaction-forces-and-temporal-kinematics-during-locomotion.pdf?origin=publication_detail

[Ted Andresen]

Re: Trying to physically verify equation for Spring Mass model

Hi Chris,

The first line of the abstract you listed led me on an enjoyable excursion to the ISS and an examination of the COLBERT or T2 in Node 3 (near the head).

Karen Nyberg does a great presentation at:

https://www.youtube.com/watch?v=_ikouWcXhd0

I knew there was a problem with the harness when “Suni” Williams ran Boston on the earlier TM in ’07.

https://en.wikipedia.org/wiki/Sunita_Williams

She gives a great tour of the station at:

https://www.youtube.com/watch?v=FXv9AZl3fw4

Doug Wheelock had some interesting comments on the nerve ending on the bottom of a crewmember’s feet:

https://www.youtube.com/watch?v=8scFoH36EmY

I worked on reentry analysis, so I was interested in the video on the ride home on the Soyuz.

https://www.youtube.com/watch?v=-l7MM9yoxII

I hope some may enjoy the above links.

Ted

[Gerrard Farrell]

Re: Trying to physically verify equation for Spring Mass model

Hi Ted
I had a look at the links and there appears to be a fair amount of overlap in our interests .
Several years ago I was pondering exercise in micro gravity ( ISS) and the ongoing problem of maintaining tissue integrity in the lower extremities . As far as I am aware this is still a problem .

Here is an extract ( spelling errors included ) from something I dreamed up as a muscle loss counter measure and posted on podiatry arena . If you used self adjusting hydraulic or pneumatic hinges to prevent excessive rates of tissue loading I still feel it might work .

At the time the idea was novel but I have seen a few similar rigs used by researchers since .-

• Hi all
  I just read through this thread and wondered if anyone had had the same thought as me .
  Why not use the muscular forces generated by one astronaut to apply force to and resist force from, the musculoskeletal system of another astronaut . In this way it may be possible to provide sufficient stimulus to avoid degradation of the various body systems .It would require a suitable framework to control the interface and the forces being applied could be measured by in-shoe instrumentation .
  Any thoughts ?
  Scotfoot
  
  Gerrard Farrell
  
  Glasgow
  scotfoot, Oct 22, 2010
  #6
• 
  scotfootWell-Known Member
  
  With regard to the previous post please consider the following .
  First take a park bench made up of wooden slats and remove the back rest section .
  Next take two individuals A and B and get them to lie flat on their backs on the bench pointing in opposite directions and with the soles of their feet touching . Next get them to inch towards each other along the bench but with the soles of their feet still touching ,till their legs bend at the knee to an angle of about 45 degrees and their legs are raised off the bench by about 40 cm or so .
  Next introduce a foot board beween the feet of A and B so that the two individuals are now separated by it . Next take a rigid pole and attatch it to the middle of the lower border of the foot board and then run it down through the slats of the bench and attatch it to the ground via a hinge which will allow movement of the footboard in a direction roughly parallel to the long axis of the bench .Finally provide handles for A and B ,attatched to the bench ,that they can grip whilst their arms are extended by their sides .A and B are now in a position to apply forces to each others musculoskeletal systems .
  The device would allow A to use both legs against one of Bs etc and could be used for eccentric and concentric exercise as well as for impact and non impact exercise .
  Large ground reaction forces could be duplicated.
  In a microgravity enviroment the anchor for the foot board pole could be provided by an extension of the main body of the framework thus providing a free floating , closed energy system tethered fore and aft to the body of a craft .
  A bench would not be required to support A and B in a microgravity enviroment and so it could be replaced by a simple framework .
  The device outlined above would weigh only a few pounds in a 1 g enviroment
  Any thoughts ?
  Scotfoot
  
  Gerrard Farrell
  
  Glasgow
  scotfoot, Oct 28, 2010
  #7
• 
  scotfootWell-Known Member
  
  Further to the previous 2 posts in this thread it may be possible to use a modified version of the exercise frame to target the peronial and tibialis posterior muscles.
  This would be achieved in the following way .
  Firstly , the pole attatching the footboard to the frame would be secured in a position perpendicular to the long axis of the frame by a locking device . Next , the pole could be continued up into a housing element in the footboard where it could be secured by a second locking device . When the lock on the pole section in the footboard is released the footboard would be able to rotate around the long axis of the pole . Subject A would then place his/her feet at on the board as far from the axis of rotation as possible to give maximum mechanical advantage . Subject B would place his/ her feet on the board close to each other and on either side of the axis . A would then rotate the footboard from side to side whilst B tried to resist the movement . This would involve many of the muscles of the body including the peroneals and tibialis posterior.
  Any thoughts ?
  
  Regards
  Gerrard Farrell
  (scotfoot)
  
  Gerrard Farrell
  
  Glasgow
  scotfoot, Nov 4, 2010
  #8
• 
  scotfootWell-Known Member
  
  Please note that in the last post "on either side of the axis " should read " on one side of, but close to the axis ".
  Gerrard Farrell
  (Scotfoot)
  
  Gerrard Farrell
  
  Glasgow

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[Edmund Cramp]

Re: Trying to physically verify equation for Spring Mass model

Chris, that's fascinating - I had never known about the jumping weights before but it reminds me of a training run I did years ago for the Pike Peak marathon - I found that I could run downhill super fast on the hairpin course by carrying a gallon jug of water and swinging it every time I went around a curve so I never had to slow down to stay on the track around the bends. Wonderful, Thank You!

[Chris Kirtley]

Re: Trying to physically verify equation for Spring Mass model

Ha! I would like to see a video of that, Edi. And surely beer would work even better than water?

[Edmund Cramp]

Re: Trying to physically verify equation for Spring Mass model

I ran for years with the Tampa Bay Hash House Harriers but that was just a vacation ... very fun going from running at sea-level to running around about 8,000 feet for a week. Almost all the serious Pikes Peak running made it up there before me but I beat just about everyone on the way back down. I ran with a water jug because that way I still had a full jug when I reached the end ...